On Harmonic Balance Method-based Lagrangian contact formulations for vibro-impact problems

This article assesses two Harmonic Balance Method-based numerical Lagrangian strategies for the characterization of periodic response a mechanical system subject to unilateral contact constraints. The model used evaluation is an academic rod facing obstacle that firstly considered as equivalent stiffness (flexible) and then rigid obstacle. Nonlinear frequency curves are obtained through arc-length continuation procedure confronted corresponding time integration simulations. An in-depth comparative analysis conducted on signals both domain strategies: (1) linear complementarity problem (LCP-HBM) (2) dynamic (DLFT-HBM). conditions thoroughly investigated in compared with reference Particular attention paid relation between methods it shown DLFT-HBM asymptotically LCP-HBM. study also shows oversampling inside alternating frequency–time procedures generates non-physical high harmonics. Finally, convergence order assess influence different parameters respect laws.